# 4. Median of Two Sorted Arrays

### Problem:

There are two sorted arrays nums1 and nums2 of size m and n respectively.

Find the median of the two sorted arrays. The overall run time complexity should be O(log (m+n)).

Example 1:

``````nums1 = [1, 3]
nums2 = [2]

The median is 2.0
``````

Example 2:

``````nums1 = [1, 2]
nums2 = [3, 4]

The median is (2 + 3)/2 = 2.5
``````

### Solutions:

``````public class Solution {
public double findMedianSortedArrays(int[] nums1, int[] nums2) {
int n = nums1.length + nums2.length;
int one = findKth(nums1, 0, nums2, 0, (n + 1)/2);
int two = findKth(nums1, 0, nums2, 0, (n + 2)/2);
return ((double)one + (double)two )/ 2.0;
}
private int findKth(int[] nums1, int s1, int[] nums2, int s2, int k) {
if (s1 >= nums1.length) {
return nums2[s2 + k - 1];
}
if (s2 >= nums2.length) {
return nums1[s1 + k - 1];
}
if (k == 1) {
return Math.min(nums1[s1], nums2[s2]);
}
int m1 = s1 + k / 2 - 1;
int m2 = s2 + k / 2 - 1;
int mid1 = 0;
int mid2 = 0;
if (m1 >= nums1.length) {
mid1 = Integer.MAX_VALUE;
}
else {
mid1 = nums1[m1];
}
if (m2 >= nums2.length) {
mid2 = Integer.MAX_VALUE;
}
else {
mid2 = nums2[m2];
}
if (mid1 < mid2) {
return findKth(nums1, m1 + 1, nums2, s2, k - k/2);
}
else {
return findKth(nums1, s1, nums2, m2 + 1, k - k/2);
}
}
}
``````